Problem

Suppose $T: V \rightarrow W$ is a linear transfor…

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Problem 43 Hard Difficulty

Prove that if $T: V \rightarrow W$ is a one-to-one linear transformation and $\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \ldots, \mathbf{v}_{k}\right\}$ is a linearly independent set of vectors in $V$, then
$$\left\{T\left(\mathbf{v}_{1}\right), T\left(\mathbf{v}_{2}\right), \ldots, T\left(\mathbf{v}_{k}\right)\right\}$$
is a linearly independent set of vectors in $W$.

Answer

linearity of $T$ and the definition of a linearly independent set.

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Algebra

Differential Equations and Linear Algebra

Chapter 6

Linear Transformations

Section 4

Additional Properties of Linear Transformations

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Video Transcript

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